Break Blade 1: Kakusei no Toki, Toaru Hikuushi e no Tsuioku Recommendations
Both give a very similar feeling. Both have futuristic monarchies that are plunged into war. Both have princesses that fall in love with their protectors despite being betrothed to a prince. The MCs are both underdogs, whether it be because of nonability or because of social class. Break Blade focuses more on the MCs fighting and struggle, while Princess and the Pilot focuses more on their romance. Break Blade can be summed up as a battle focused Princess and the Pilot with mechs. Vice versa, Princess and the pilot is a romance focused Break Blade with fighter planes.